# Why are policy iteration and value iteration studied as separate algorithms?

In Sutton and Barto's book about reinforcement learning, policy iteration and value iterations are presented as separate/different algorithms.

This is very confusing because policy iteration includes an update/change of value and value iteration includes a change in policy. They are the same thing, as also shown in the Generalized Policy Iteration method.

Why then, in many papers as well, they (i.e. policy and value iterations) are considered two separate update methods to reach an optimal policy?

Value iteration, in contrast, does not use that insight. It just updates estimates of the values of being in the states one step at a time. If these values are initialized at 0, you can think of this of the $$i$$th iteration computing the value of what would be the optimal policy if we knew the MDP would end after $$i$$ iterations. We never really have to think explicitly about policies (though we are in effect computing a policy each iteration), and never directly calculate the infinite sum of expected discounted rewards.